I had to do a double take when I saw this.

I really don't see how it could be in there that tight, there are no marks on any of the edges.
First attempt I am going to cut a notch across the top, and hit it with a twist impact screwdriver.
Second attempt notch an edge and try to spin it off, with an air chisel.
Third attempt I might weld a nut to the top of the bolt.
I think last resort is cut the head off.
Imo 1st I'd notch it and try a flat head screwdriver if that dont work I'd try to drill it a little and try an easy out. Then weld a nut. Last resort cut the head off and try to get the remaining stud loose. I have removed alot of broken bolts from working on guns mostly small scope base screws. But an easy out will always do the trick when a simple slot and punch wont! But I'm sure a head bolt has alot more torque than a scope base screw.